Solution to Schrodinger’s equation using random walk

Abstract

In this paper, the random walk method is used to solve the equation of Schrodinger for different potentials, this method was introduced by Anderson (Anderson, 1975). To calculate the fundamental energy of molecules, this method is also known as Monte Carlo diffusive and proven to be very useful in different areas of quantum mechanics (Gould & Tobochnik, 2012), (Curotto, 2010). The fundamental energy is calculated for a one-dimensional harmonic oscillator and in three dimensions, the fundamental energy for the Morse potential, cosine potential hyperbolic, and polynomial potential of order four, which are potential modeling diatomic molecules. The main objective of the revision of this method is to provide the students a simple algorithm of how to apply this Monte Carlo method to a typical problem of quantum mechanics.